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Maximum likelihood estimation in semiparametric regression models with censored data

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  • D. Zeng
  • D. Y. Lin
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    Abstract

    Semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies. The presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models. We present several classes of semiparametric regression models, which extend the existing models in important directions. We construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters. The maximum likelihood estimators are consistent and asymptotically normal with efficient variances. We develop simple and stable numerical techniques to implement the corresponding inference procedures. Extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings. Applications to three medical studies yield important new insights. We conclude that there is no reason, theoretical or numerical, not to use maximum likelihood estimation for semiparametric regression models. We discuss several areas that need further research. Copyright 2007 Royal Statistical Society.

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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

    Volume (Year): 69 (2007)
    Issue (Month): 4 ()
    Pages: 507-564

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    Handle: RePEc:bla:jorssb:v:69:y:2007:i:4:p:507-564

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    Cited by:
    1. Amélie Detais & Jean-François Dupuy, 2011. "Maximum likelihood estimation in a partially observed stratified regression model with censored data," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 63(6), pages 1183-1206, December.
    2. Antonio Lijoi & Bernardo Nipoti, 2013. "A class of hazard rate mixtures for combining survival data from different experiments," DEM Working Papers Series 059, University of Pavia, Department of Economics and Management.
    3. Mondal, Shoubhik & Subramanian, Sundarraman, 2014. "Model assisted Cox regression," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 123(C), pages 281-303.
    4. Pao-sheng Shen, 2014. "Semiparametric regression analysis for clustered doubly-censored data," Computational Statistics, Springer, Springer, vol. 29(3), pages 813-828, June.
    5. Pao-sheng Shen, 2012. "Analysis of left-truncated right-censored or doubly censored data with linear transformation models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, Springer, vol. 21(3), pages 584-603, September.
    6. Guoqing Diao & Guosheng Yin, 2012. "A general transformation class of semiparametric cure rate frailty models," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 64(5), pages 959-989, October.
    7. Pao-sheng Shen, 2011. "Semiparametric analysis of transformation models with left-truncated and right-censored data," Computational Statistics, Springer, Springer, vol. 26(3), pages 521-537, September.
    8. Wen, Chi-Chung & Chen, Yi-Hau, 2011. "Nonparametric maximum likelihood analysis of clustered current status data with the gamma-frailty Cox model," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 55(2), pages 1053-1060, February.
    9. Chi-Chung Wen, 2010. "Semiparametric maximum likelihood estimation in Cox proportional hazards model with covariate measurement errors," Metrika, Springer, Springer, vol. 72(2), pages 199-217, September.

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